<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="cqc_lang.html#NM2">CQC-variable_list</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="valuat_1.html#K2">Valuations_in</a> <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="sublemma.html#NM1">Val_Sub</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>













<b>assume </b><a NAME="E1:91"/><i><font color="Green">E74</font></i>: 
( ( for <font color="Olive">b<sub>1</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font> holds <br/> not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K22">still_not-bound_in</a> <font color="Maroon">c<sub>3</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="qc_lang1.html#NM3">bound_QC-variable</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> holds <br/><font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> ) &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="xboole_0.html#R1">misses</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<a NAME="E2:91"/><i><font color="Green">E75</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="valuat_1.html#D8">VALUAT_1:def 8</a></i>;<br/>
<a NAME="E3:91"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:91_1"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:91_1"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="sublemma.html#E2:91"><i><font color="Green">E75</font></i></a>, <a class="txt" href="sublemma.html#E1:91_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/>
<a NAME="E3:91_1"/><i><font color="Green">E78</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T44">RELAT_1:44</a></i>;<br/>
<div><i><font color="Green">E79</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_1_1"/><i><font color="Green">E80</font></i>: 
not <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 ;<br/><a NAME="E2:91_1_1"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T13">FUNCT_4:13</a></i>;<br/><a NAME="E3:91_1_1"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="funct_4.html#T13">FUNCT_4:13</a></i>;<br/><a NAME="E4:91_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><a NAME="E5:91_1_1"/><b>then </b><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 ;<br/><a NAME="E6:91_1_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:91"><i><font color="Green">E75</font></i></a>, <a class="txt" href="sublemma.html#E1:91_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E7:91_1_1"/><b>then </b><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E5:91_1_1"><i><font color="Green">E81</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/><a NAME="E8:91_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:91_1_1"><i><font color="Green">E80</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><a NAME="E9:91_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 ;<br/><b>hence </b><a NAME="E10:91_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:91_1"><i><font color="Green">E77</font></i></a>, <a class="txt" href="sublemma.html#E7:91_1_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_1_2"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 ;<br/><b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> as   <a href="qc_lang1.html#NM3">bound_QC-variable</a> <b>by </b><i><a class="txt" href="sublemma.html#E2:91_1"><i><font color="Green">E77</font></i></a>, <a class="txt" href="sublemma.html#E3:91_1"><i><font color="Green">E78</font></i></a>, <a class="ref" href="sublemma.html#T5" target="_self">Th5</a></i>;<br/><div><i><font color="Green">E81</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_1_2_1"/><i><font color="Green">E82</font></i>: 
not <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:91_1_2_1"/><b>then </b><i><font color="Green">E83</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:91_1_2"><i><font color="Green">E80</font></i></a>, <a class="ref" href="funct_4.html#T13">FUNCT_4:13</a></i>;<br/><a NAME="E3:91_1_2_1"/><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:91_1_2_1"><i><font color="Green">E82</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><div><i><font color="Green">E85</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_1_2_1_1"/><i><font color="Green">E86</font></i>: 
not <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:91_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:91_1_2_1"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><a NAME="E3:91_1_2_1_1"/><b>then </b><i><font color="Green">E87</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:91_1_2"><i><font color="Green">E80</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/><a NAME="E4:91_1_2_1_1"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:91_1_2_1"><i><font color="Green">E83</font></i></a>, <a class="txt" href="sublemma.html#E1:91_1_2_1_1"><i><font color="Green">E86</font></i></a>, <a class="ref" href="funct_4.html#T13">FUNCT_4:13</a></i>;<br/><a NAME="E5:91_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:91_1_2_1_1"><i><font color="Green">E87</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/><a NAME="E6:91_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E7:91_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E8:91_1_2_1_1"/><b>then </b><i><font color="Green">E88</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:91_1"><i><font color="Green">E77</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/><a NAME="E9:91_1_2_1_1"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:91"><i><font color="Green">E75</font></i></a>, <a class="txt" href="sublemma.html#E1:91_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E10:91_1_2_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E8:91_1_2_1_1"><i><font color="Green">E88</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_1_2_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:91_1_2_1_2"/><b>then </b><i><font color="Green">E86</font></i>: 
not <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K22">still_not-bound_in</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:91"><i><font color="Green">E74</font></i></a></i>;<br/><a NAME="E3:91_1_2_1_2"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="substut1.html#T34">SUBSTUT1:34</a></i>;<br/><a NAME="E4:91_1_2_1_2"/><b>then </b>
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a>  )
 <b>by </b><i><a class="txt" href="sublemma.html#E1:91_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:91_1_2_1_2"/><i><font color="Green">E87</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp; 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a>  )
 ;<br/><a NAME="E7:91_1_2_1_2"/>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> : ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang1.html#K2">bound_QC-variables</a>  ) </span>}</span> 
 <b>by </b><i><a class="txt" href="sublemma.html#E6:91_1_2_1_2"><i><font color="Green">E87</font></i></a></i>;<br/><a NAME="E8:91_1_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="qc_lang3.html#K1">variables_in</a> <font color="Maroon">c<sub>3</sub></font>,<a href="qc_lang1.html#K2">bound_QC-variables</a> 
 <b>by </b><i><a class="ref" href="qc_lang3.html#D2">QC_LANG3:def 2</a></i>;<br/><b>hence </b><a NAME="E9:91_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="sublemma.html#E2:91_1_2_1_2"><i><font color="Green">E86</font></i></a>, <a class="ref" href="qc_lang3.html#T6">QC_LANG3:6</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E6:91_1_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E4:91_1_2_1"><i><font color="Green">E85</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_1_2_2"/><i><font color="Green">E82</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/><a NAME="E2:91_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/><a NAME="E3:91_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:91"><i><font color="Green">E74</font></i></a>, <a class="txt" href="sublemma.html#E1:91_1_2_2"><i><font color="Green">E82</font></i></a></i>;<br/><a NAME="E4:91_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:91_1_2"><i><font color="Green">E80</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>;<br/><a NAME="E5:91_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E6:91_1_2_2"/><b>then </b><i><font color="Green">E83</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:91_1"><i><font color="Green">E77</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/><a NAME="E7:91_1_2_2"/>
not <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E1:91"><i><font color="Green">E74</font></i></a>, <a class="txt" href="sublemma.html#E1:91_1_2_2"><i><font color="Green">E82</font></i></a>, <a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/><a NAME="E8:91_1_2_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>;<br/><a NAME="E9:91_1_2_2"/><b>then </b><i><font color="Green">E84</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font>
 ;<br/><a NAME="E10:91_1_2_2"/>
<font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:91"><i><font color="Green">E75</font></i></a>, <a class="txt" href="sublemma.html#E1:91_1"><i><font color="Green">E76</font></i></a>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><b>hence </b><a NAME="E11:91_1_2_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E6:91_1_2_2"><i><font color="Green">E83</font></i></a>, <a class="txt" href="sublemma.html#E9:91_1_2_2"><i><font color="Green">E84</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:91_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E3:91_1_2"><i><font color="Green">E81</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:91_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E4:91_1"><i><font color="Green">E79</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:91"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="sublemma.html#K1" target="_self">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="sublemma.html#K15" target="_self">+*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span> <a href="valuat_1.html#K8">*'</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="sublemma.html#E2:91"><i><font color="Green">E75</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/>


</div>
